Journal Jack William Bell's Journal: Light Speed! 16
Ever have trouble envisioning the effects of relativistic speeds on objects? Light Speed! is a Linux-based Open-GL program that simulates contraction, red/blue shift and other strange things which occur when an object aproaches lightspeed. Note that if you were standing next to the object and going the same speed, everything would look normal to you, but the rest of the universe would be distorted.
Now for a quick test to see if you actually understand this aspect of special relativity. Object A is moving at lightspeed ("C") in one direction and object B is moving at C in the other direction. They are approaching each other. What is their relative velocity? Is it:
- Zero
- C
- C * 2
- C squared
- None of the above
OK, same question but they have passed and are now moving away from each other.
Easy (Score:2)
That's easy. 5 (None of the above) because they are outside of each other's light cones (and thus an observer on one can't even know of the other, let alone measure a "relative" velocity.)
After they pass, their relative velocity is C.
Note, both of these answers are correct according to GR, but have not been tested. Since GR isn't consistent with QM (which has much more experemental evidence to back it), and GR isn't the only theory to produce results consistent with what data we do have, I don't take G
Re: (Score:1)
Re:Easy (Score:2)
Well, my question is why do you need light to mesure the relative velocitys? The question also did not say the observer was on one.
You don't need light per se, but you do need to be able to detect something by some means in order to measure its velocity. By the cannon, you can't even know of the existence of something aproaching you at light speed, because nothing can move fast enough to get the message to you (by the time the message gets to you, the object will have already passed you).
As for your s
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Re:Easy (Score:2)
Can't you calculate the relative velocity of two objects based on the relative velocitys from a third perspective? I think one can.
Correct. And in this case you'll get an imaginary number (because four-vectors work like quaternions [wolfram.com]), meaning their relative velocity is undefined.
-- MarkusQ
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the 'Cheating Observer' aka the 'Train Schedule' (Score:2)
For the sake of a thought experiment let us say that we can treat our two relativistic objects (A and B) as being like trains. They are on parallel tracks and they are on a schedule. Because we know the schedule and their speed we know where they are and ho
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Re:the 'Cheating Observer' aka the 'Train Schedule (Score:2)
In any case, according to special relativity the answer is C. This is because according to SR nothing can move relative to another object faster than C! So what happens is that the strange effects mentioned in the parent post kick in. As a result you get inifinite red/blue shifting (depending upon whether the objects are ap
Re:the 'Cheating Observer' aka the 'Train Schedule (Score:2)
Boosting something to a significant percentage of C isn't that hard, it would only require a few grams of anti-matter. It is reaching in the the 99.9 percentile of C that is hard because the mass effects of SR really start to ramp up as you close in on the last few tenths of a percent.
Re:the 'Cheating Observer' aka the 'Train Schedule (Score:1)
To be pedantic (since we ARE talking about GR here), the relative velocity here isn't actually 100 MPH. It's very slightly less -- somewhere around 99.99999 MPH. This is the difference between classical and relativistics dynamics.
I wouldn't mention it, but this is the entire reason why the answer is so different and counter-intuitive for the case where the velocities of the objects approach c. The difference
Re:Easy (Score:2)
Still, you do get the prize for the most correct possible answer. I was also willing to accept [2] for both and [5] for bo
Re:Easy (Score:2)
The main reason I treat it as just a "reasonable working hypothosis" is that it is only one of serveral theories that fit the data we have; the fact that it is the accepted theory has more to do with the whims of history than anything else. To get a feeling for why it's not "the only possible answer" consider
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Hard (Score:2)
I tagged Jack's initial question as easy, because it was of the form "what does theory X say about topic Y"
What you are asking is hard, because it is the form "if what we presently believe turns out to be false, what will the real answer say about topic Y" -- obviously a much harder question. So here are a few different answers:
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